An assessment of some effects of the nonsmoothness of the Leishman–Beddoes dynamic stall model on the nonlinear dynamics of a typical aerofoil section

We investigate the dynamic behaviour of the typical airfoil section modelled structurally by linear springs in pitch and plunge with the aerodynamic loading represented by our interpretation of the state-space version of the Leishman–Beddoes semi-empirical model. Similarly to other semi-empirical models of dynamic stall, this model represents the nonlinear component of the unsteady aerodynamic loading on the airfoil by a series of equations, with empirical coefficients, devised specifically for each of the relevant dynamic stall flow states. Given this piecewise definition of the loading, we pay particular attention to the description of the discontinuities of the model and to their effect on the dynamics of the system through phase plots, Poincaré sections and bifurcation diagrams. These results show that the model is sensitive to small variations of some of the parameters of the model. They also show that prohibitively small timesteps are required to obtain numerically converged Poincaré maps. We advocate the use of event detection techniques for the numerical integration of the equations of motion to reduce this severe timestep restriction.